Observations of quasi-periodic oscillations (QPOs) in X-ray binaries hold a key to understanding many aspects of these enigmatic systems. Complex appearance of the Fourier phase lags related to QPOs is one of the most puzzling observational effects in accreting black holes. In this Letter we show that QPO properties, including phase lags, can be explained in a framework of a simple scenario, where the oscillating media provides a feedback on the emerging spectrum. We demonstrate that the QPO waveform is presented by the product of a perturbation and a time delayed response factors, where the response is energy dependent. The essential property of this effect is its non-linear and multiplicative nature. Our multiplicative reverberation model successfully describes the QPO components in energy dependent power spectra as well as the appearance of the phase lags between signal in different energy bands. We apply our model to QPOs observed by Rossi X-ray Timing Explorer in BH candidate XTE J1550-564. We briefly discuss the implications of the observed energy dependence of the QPO reverberation times and amplitudes to the nature of the power law spectral component and its variability.